No. In fact, it was Sauron's rising that prompted Gandalf to find a way to re-take Erebor and remove Smaug from the possible use by Sauron.
LOTR, Appendix A Annals of the Kings and Rulers:
But at last there came about by chance a meeting between Gandalf and
Thorin that changed all the fortunes of the House of Durin, and led to
other and greater ends beside. On a time Thorin, returning west from a
journey, stayed at Bree for the night. There Gandalf was also. He was
on his way to the Shire, which he had not visited for some twenty
years. He was weary, and thought to rest there for a while.
many cares he was troubled in mind by the perilous state of the North;
because he knew then already that Sauron was plotting war, and
intended, as soon as he felt strong enough, to attack Rivendell. But
to resist any attempt from the East to regain the lands of Angmar and
the northern passes in the mountains there were now only the Dwarves
of the Iron Hills. And beyond them lay the desolation of the Dragon.
The Dragon Sauron might use with terrible effect. How then could the
end of Smaug be achieved?
If Bilbo had stayed home it's likely that the Ring would have been found by some Orc:
LOTR, Book I, Ch. 2 The Shadow of the Past:
The Ring was trying to get back to its master. It
had slipped from Isildur’s hand and betrayed him; then when a chance
came it caught poor Déagol, and he was murdered; and after that
Gollum, and it had devoured him. It could make no further use of him:
he was too small andmean; and as long as it stayed with him he would
never leave his deep pool again. So now, when its master was awake
once more and sending out his dark thought from Mirkwood, it abandoned
Gollum. Only to be picked up by the most unlikely person imaginable:
Bilbo from the Shire!
Sauron was already rising well before Gandalf joined up with Thorin. And the Ring had abandoned Gollum some time before Bilbo found it.